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complib/dspgst(3) -- reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
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DSPGST reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. B must have been previously factorized as U**T*U or L*L**T by DPPTRF.... |
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complib/dspgv(3) -- a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(l
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DSPGV computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric, stored in packed format, and B is also positive definite. |
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complib/dsprfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefin
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DSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution. |
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complib/DSPSL(3) -- DSISL solves the double precision symmetric system A * X = B using the factors computed by DSPFA.
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On Entry AP DOUBLE PRECISION(N*(N+1)/2) the output from DSPFA. N INTEGER the order of the matrix A . KPVT INTEGER(N) the pivot vector from DSPFA. B DOUBLE PRECISION(N) the right hand side vector. On Return B the solution vector X . Error Condition A division by zero may occur if DSPCO has set RCOND .EQ. 0.0 or DSPFA has set INFO .NE. 0 . To compute INVERSE(A) * C where C is a matrix with P columns CALL DSPFA(AP,N,KPVT,INFO) IF (INFO .NE. 0) GO TO ... DO 10 J = 1, P CALL DSPSL(AP,N,KPVT,C(1,J)) 1... |
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complib/dspsv(3) -- = B,
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DSPSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to s... |
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complib/dspsvx(3) -- X and B are N-by-NRHS matrices
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DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
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complib/dsptrd(3) -- reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal simila
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DSPTRD reduces a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T. |
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complib/dsptrf(3) -- packed format using the Bunch-Kaufman diagonal pivoting method
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DSPTRF computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method: A = U*D*U**T or A = L*D*L**T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. |
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complib/dsptri(3) -- compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*
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DSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. |
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complib/dsptrs(3) -- solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the fa
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DSPTRS solves a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. |
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complib/dstebz(3) -- compute the eigenvalues of a symmetric tridiagonal matrix T
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DSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix T. The user may ask for all eigenvalues, all eigenvalues in the half-open interval (VL, VU], or the IL-th through IU-th eigenvalues. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that. See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix", Report CS41, C... |
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complib/dstedc(3) -- compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and c
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DSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric matrix can also be found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the ... |
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complib/dstein(3) -- compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, usin
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DSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5). |
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complib/dsteqr(3) -- compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL
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DSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form. |
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complib/dsterf(3) -- the Pal-Walker-Kahan variant of the QL or QR algorithm
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DSTERF computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm. |
